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Physical Review A

Noise mitigation for high-sensitivity phase estimation based on weak measurements

Xiaorui Tan, Hongjing Li, Qi Song, Chunhui Shi, Qingxin Deng, Binke Xia, Zhongyuan Luo, Jingzheng Huang, Guihua Zeng

Published May 8, 2024• 3 citations
Publisher

Abstract

Phase estimation has attracted much attention in the field of sensing, where weak measurement has become an effective solution for the study of small physical quantities because of its anomalous amplification property. However, it is difficult for weak measurement to cope with large low-frequency noise signals in the environment due to its extremely narrow linear range, which makes the extension of weak measurement to practical applications a challenging task. In order to solve this issue, we propose and experimentally verify a phase demodulation scheme based on weak measurement, which solves the problem of working point offset caused by the noise through artificially introducing a high-frequency carrier and performing demodulation operations on the output light. The experimental results show that the scheme can improve the signal-to-noise ratio by 17 dB compared to standard weak measurement and ensures low distortion in phase demodulation. Moreover, the scheme is not limited to a specific modulation depth, which greatly improves the robustness of the scheme.

DOI
10.1103/physreva.109.053512

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Phase estimation has attracted much attention in the field of sensing, where weak measurement has become an effective solution for the study of small physical quantities because of its anomalous amplification property. However, it is difficult for weak measurement to cope with large low-frequency noise signals in the environment due to its extremely narrow linear range, which makes the extension of weak measurement to practical applications a challenging task. In order to solve this issue, we propose and experimentally verify a phase demodulation scheme based on weak measurement, which solves the problem of working point offset caused by the noise through artificially introducing a high-frequency carrier and performing demodulation operations on the output light. The experimental results show that the scheme can improve the signal-to-noise ratio by 17 dB compared to standard weak measurement and ensures low distortion in phase demodulation. Moreover, the scheme is not limited to a specific modulation depth, which greatly improves the robustness of the scheme.
Weak value amplification has been applied to various small physical quantities estimation, however there still lacks a practical feasible protocol to amplify ultra-small longitudinal phase, which is of importance in high precision measurement. Very recently, a different amplification protocol within the framework of weak measurements is proposed to solve this problem, which is capable of measuring any ultra-small longitudinal phase signal that conventional interferometry tries to do. Here we experimentally demonstrate this weak measurements amplification protocol of ultra-small longitudinal phase and realize one order of magnitude amplification in the same technical condition, which verifies the validity of the protocol and show higher precision and sensitivity than conventional interferometry. Our results significantly broaden the area of applications of weak measurements and may play an important role in high precision measurements.
We theoretically propose and experimentally demonstrate a modulated weak measurement scheme that permits a precise estimation of the extended phase shift. By choosing the frequency and the total post-selected light intensity as the input and output meter variables, respectively, a linear weak measurement model is established that is especially applicable to precise phase estimation. By performing a time-delay-dependent modulation strategy based on the feedback modulation of the experimental outcome, both the high phase-sensitivity and measurement precision can be retained. We have achieved a precision at the order of ∼10−5 rad that can be effectively retained with an increase in the measured phase.
Weak measurement amplification, which is considered as a very promising scheme in precision measurement, has been applied to various small physical quantities estimations. Since many physical quantities can be converted into phase signals, it is interesting and important to consider measuring small longitudinal phase shifts by using weak measurement. Here, we propose and experimentally demonstrate a novel weak measurement amplification-based small longitudinal phase estimation, which is suitable for polarization interferometry. We realize one order of magnitude amplification measurement of a small phase signal directly introduced by a liquid crystal variable retarder and show that it is robust to the imperfection of interference. Besides, we analyze the effect of magnification error which is never considered in the previous works, and find the constraint on the magnification. Our results may find important applications in high-precision measurements, e.g., gravitational wave detection.
Weak measurement is employed to measure faint signals due to its capability to amplify detection results above technical noise. However, achieving high amplification effects requires accurate adjustment to the experimental system. Estimating unknown time-varying phases, accurately estimating phases, and sensitively perceiving phase changes pose challenges, demanding the system to continuously remain at the appropriate working range. To address this issue, we propose a neural network-based adaptive weak measurement scheme via single-channel light intensity detection. Through machine learning calibrating the experimental system, the reference phase can be dynamically and accurately adjusted, accommodating time-varying phase changes and ensuring the system operates optimally. Compared with traditional dual-channel weak measurement systems, the scheme reduces experimental complexity. Meanwhile, by accurately adjusting the reference phase, the scheme has higher sensitivity and estimation precision compared to the non-modulated scheme. We validate the effectiveness of the scheme in estimating the period and stochastic time-varying phase. The proposed method highlights the advancement of machine learning in weak measurement systems and can also be applied to other quantum-enhanced measurement schemes.
We derive a general theory for the joint weak measurement with arbitrary postselection and employ it in the time-delay measurement. Especially, we study two special cases, i.e., the balanced and unbalanced postselection regimes, and present an experiment to verify the theoretical results. The experimental results show that under similar conditions, the signal-to-noise ratio of using joint weak measurement scheme remains higher than 12 dB when the measured time-delay is smaller the ultimate precision limit of the weak-value amplification scheme. Moreover, the joint weak measurement scheme is robust to the misalignment errors and the wavelength-dependency of optical components, which indicates its advantage of improving the measurement precision with convenient laboratory equipments.
We propose a scheme called difference weak measurement, and we illustrate its advantages for measuring a small longitude phase shift in high precision. Compared to the standard interferometry and standard weak measurement schemes, the proposed scheme has a much higher resolution in the presence of various practical imperfections, such as alignment error and light intensity variation error. Moreover, we highlight the advantage of utilizing a complex weak value, where its imaginary part can reduce the harmful effect induced by channel decoherence. Finally, we propose a closed-loop scenario to solve the narrow dynamic range problem that exists in the current weak measurement schemes. The difference weak measurement scheme simultaneously fulfills the requirements of high precision, wide dynamic range, and strong robustness, which makes it a powerfully practical tool for phase-shift measurement and other metrological tasks.